1.2 Function Notation - Notes [Teacher]

[1.2] FUNCTION NOTATIONWHAT IS FUNCTION NOTATION?Functions are given letter names.The names are of the form f(x) which is read "fofx". The letter inside the parentheses,usually X, stand for the domain set.The entire symbol, usually f(x), stands for the range set.The ordered-pair numbers become (x, f(x)).Function NotationFunction NotationWritten as anWritten inExample:f(x) = 3x + 1f(x)f(3)EquationFunction Notationname of functionRead: "fof xRead: T of 3"(f of x)y=5xf(x) = 5xInputoutputThink: "the output ofThink: "the output of f(domain) (range)for the input x"for the input 3"y=x+7g(x) = x + 7f(2)=3(2)+1=7f(-4)=3(-4)+1=11y=x2h(x) = xEXAMPLE #1: DETERMINE f(-2) FOR EACH FUNCTIONa.f(x) = 2x-4b.f(x)=3x2-x+7c.f(x)= 11d.f(x)=2x.f(-2)=2(-2)-4f(2)=11f(-2)=2(-2)f(-2)==8fe-2)=12+2+7(-2,11)(-2)2-3(-2,-8)=(x,y)f(-2) = 21 (242)Constant function4-3EXAMPLE #2 USING ALGEBRAIC EXPRESSION IN FUNCTIONSConsider the following functions: f(x) = x2 - 3x and g(x) = 1-2xa. Show: f(2)>g(2)Fcx)=x-3x2g(x) 1-2x 1 f(2)= = -2(12)=(2)-2(2) 1 (g(2)==31:0f(2) = 4-6Ig(2) = 1-41(c2)7g(2)f(2)===21g(2) =-31(2,-2)I11(2,3) [1.2] FUNCTION NOTATIONb. Determine: g(3b)f(3b)1g(x)=1-2x1 =:f(36) = (3b) 2-3(3b) I(9(36)=1-2(3b)(9(36)=1-66 =f(3b) = 326-96 Factoredf(3b) 962-96C. Determine:f(c+2)-g(c+2)H(33) 96(6-1),== [c7+4c+4-3c-6)]- - [1-2c-4)== -= C2+3c+1EXAMPLE #3: CONECTING FUNCTION NOTATION TO A GRAPHg(x) = vx+10For the following function, determine:FUNCTION NOTATIONDESMOSa. g(3)Cg(3) =(3.2)913)=V4g(3)=2(3,2) t point0342 [1.2] FUNCTION NOTATIONb. g(-1)g(+)==V(H)+1g(-))= to(-1,0)EP pointg(+)=0(-1.0)Oc.xifg(x) = 1y=1-11=Vx+11=x+1(o. 1)O=XVI= VXH(0,1) p pointO1=x+11d. Domain & Range of g(x)D= EXER/X-13R = EYER14203EXAMPLE #4: DETERMINE TEMPERATURE IN THE EAST RAND & WESTERN MINESThe deepest mine the in the world, East Rand mine in South Africa, reaches 3585 metersinto the Earth's Crust. Another South African mine, Western Deep, is being deepened to4100 meters. Suppose the temperature at the top of the mine shaft is 11°C and that isincreases at a rate of 0.015°C per meter as you descend.a. Represent the temperature in a mine shaft with a function. Explain why yourrepresentation is function and write it in function notation.Temperature Equation -> T = :11+0.015₫'T' represents temperature in degrees and 'd' represent degrees in Celsius.Ted) = 0.015d +11 & Function Notation3 [1.2] FUNCTION NOTATIONb. Use your function to determine the temperature at the bottom of the East Rand &Western mines.EAST RAND MINETEMPERATUREDESMOST(3585)80T(3585)=0.015(3585)+1(3583. 64.775)60= : 53.775+1140= 64.77520(0.11)( 3585, 64.775)01000200030004000TDepth Temp WESTERN MINETEMPERATUREDESMOST(4100)80TC4100) = 0.015 ( 4100) +11(3585. 64.775)(4100.725)60=61.5 +1140= 72.520( 4100 72.5)(0.11)10002000300040005000Depta TempEXAMPLE #5: TEMPERATURE OF A DEEP LAKEThe temperature if the water at the surface of a deep lake is 22°C on a warm summer's day.As Renaldo Scuba dives to the depths of the lake, he finds that the temperature decreasesby 1.5°C for every 8 meters he descends.a. Model the water temperature at any depth using function notation.Let "d" represent depth, in meters, below Serface of lakelet "T" represent temperation, in degree alcius, at depth thisT(d)=22-15(1)4 [1.2] FUNCTION NOTATIONb. Use the function from (a) to determine the water temperature at depth of 40 meters.T(46)=22-15(40)(0.22)20T146)=22-7.515(40. 14.5)T(40) = 14.510(40,14.5)5is The temp. at a deptacto2004004um is 14.5°Cc. At what depth is the temperature is 5.5°C?y=5.( ?,5.5)-22 -22(0.22)5.5=22-1.5(d)20-16.5==-1.5dg: The temp.15is 5.5°c at-132=====a depthot10-1.5 -1/588m(ss. 5.5)588=d(88,5.5)O200d. How deep is the lake?y=0 (?,0)D-176 = -Vsd io The lake-1.5 -1/.5is approx0=22-1.5(%)352 =d 117m.3-22=-15don8117.3 - (117,3,6)5=